Duty engineer was an engineering officer in Starfleet who acted as the duty officer when the chief engineer was off-duty.
On the USS Enterprise-D, in 2367, the duty engineers for the third shift were MacDougal and Leland T. Lynch. (TNG-R: "Galaxy's Child")
In 2369, Chief Engineer Geordi La Forge requested a display of the Engineering Department Duty Roster for the next three days. The names of duty engineers for each of the duty shifts were listed in this roster. (TNG-R: "Aquiel")